Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19097717 | C2 | semidirect |
| 4. #23757098 | C2 | semidirect |
| 5. #23757077 | C2 | semidirect |
| 6. #23757076 | C2 | semidirect |
| 58. C22×C157 | Q32 | semidirect |
| 71. C157 | #2216 | semidirect |
| 130. C22 | #19097717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097717 | 2 |
| C22×#14578929 | 2 |
| #23757514 | 2 |
| #23757098 | 2 |
| #23757077 | 2 |
| #23757076 | 2 |
| #467×C157 | 2 |
| #2216 | 157 |